Friedman, S-D, Rathjen, M and Weiermann, A (2013) Slow consistency. Annals of Pure and Applied Logic, 164 (3). 382 - 393 (12). ISSN 0168-0072
Abstract
The fact that "natural" theories, i.e. theories which have something like an "idea" to them, are almost always linearly ordered with regard to logical strength has been called one of the great mysteries of the foundation of mathematics. However, one easily establishes the existence of theories with incomparable logical strengths using self-reference (Rosser-style). As a result, PA+. Con(PA) is not the least theory whose strength is greater than that of PA. But still we can ask: is there a sense in which PA+. Con(PA) is the least "natural" theory whose strength is greater than that of PA? In this paper we exhibit natural theories in strength strictly between PA and PA+ Con(PA) by introducing a notion of slow consistency.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2013, Elsevier Masson. This is an author produced version of a paper published in Annals of Pure and Applied Logic. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Peano arithmetic, consistency strength, interpretation, fast growing function, slow consistency, Orey sentence |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 28 Feb 2013 11:08 |
Last Modified: | 31 Oct 2016 17:31 |
Published Version: | http://dx.doi.org/10.1016/j.apal.2012.11.009 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.apal.2012.11.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:75180 |